Computing and Partitioning Cloud Feedbacks using Cloud. Property Histograms. Part II: Attribution to Changes in Cloud Amount, Altitude, and

Transcription

1 Generated using version 3.0 of the official AMS L A TEX template 1 2 Computing and Partitioning Cloud Feedbacks using Cloud Property Histograms. 3 Part II: Attribution to Changes in Cloud Amount, Altitude, and 4 Optical Depth 5 Mark D. Zelinka Department of Atmospheric Sciences, University of Washington, Seattle, Washington, and Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Livermore, California 6 Stephen A. Klein Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory, Livermore, California 7 Dennis L. Hartmann Department of Atmospheric Sciences, University of Washington, Seattle, Washington Corresponding author address: Mark D. Zelinka, Program for Climate Model Diagnosis and Intercomparison Lawrence Livermore National Laboratory 7000 East Avenue, L-103 Livermore, CA zelinka1@llnl.gov 1

2 8 ABSTRACT Cloud radiative kernels and histograms of cloud fraction, both as functions of cloud top pressure and optical depth, are used to quantify cloud amount, altitude, and optical depth feedbacks. The analysis is applied to doubled CO 2 simulations from eleven global climate models in the Cloud Feedback Model Intercomparison Project. Global, annual, and ensemble mean longwave (LW) and shortwave (SW) cloud feedbacks are positive, with the latter nearly twice as as large as the former. The robust increase in cloud top altitude is the dominant contributor to the positive LW cloud feedback. The negative impact of reductions in cloud amount offsets more than half of the positive impact of rising clouds on LW cloud feedback, but the magnitude of compensation varies considerably across models. In contrast, robust reductions in cloud amount make a large and virtually unopposed positive contribution to SW cloud feedback, though the inter-model spread is greater than for any other individual feedback component. Overall reductions in cloud amount have twice as large an impact on SW fluxes as on LW fluxes such that the net cloud amount feedback is moderately positive, with no models exhibiting a negative value. As a consequence of large but partially offsetting effects of cloud amount reductions on LW and SW feedbacks, both the mean and inter-model spread in net cloud amount feedback are smaller than those of the net cloud altitude feedback. Finally, we find that the large negative cloud feedback at high latitudes results from robust increases in cloud optical depth, not from increases in total cloud amount as is commonly assumed. 1

3 28 1. Introduction Since the early days of climate modeling it has been recognized that changes in clouds that accompany climate change provide a feedback through their large impact on the radiation budget of the planet. Schneider and Dickinson (1974) noted that accurate assessment of cloud feedback requires quantifying the spatially-varying role of changes in cloud amount, altitude, and optical properties on both shortwave (SW) and longwave (LW) radiation and that even subtle changes to any of these properties can have significant effects on the planetary energy budget. Schneider (1972) performed one of the first investigations into the role of clouds as feedback mechanisms, focusing on hypothetical changes in cloud amount and altitude. His calculations showed that a negative feedback would be produced at most latitudes from an increase in low and middle-level clouds if albedo and altitude were held fixed but that this effect could largely be cancelled by the enhanced cloud greenhouse effect caused by a rise in global mean cloud top altitude of only a few tenths of a kilometer, a result also supported by Cess (1974) and Cess (1975). Other early studies focused on the potential increase in cloud optical depth that would occur in association with global warming. Paltridge (1980), using the relationship between cloud optical depth and liquid water path derived by Stephens (1978), showed that increases in liquid water path would tend to strongly increase the amount of reflected SW radiation more than it would decrease the amount of emitted LW radiation, resulting in a large negative feedback on a warming climate. These results were reinforced in the study of Somerville and Remer (1984), who derived a large negative optical depth feedback using a 1-D radiative-convective equilibrium model with empirically derived relations between temperature and cloud water content measured by aircraft over 2

4 the former Soviet Union (Feigelson (1978)). Although 1-D radiative-convective equilibrium models employed to quantify cloud feedback in early studies like those described above provide insight into potential cloud feedbacks, the cloud feedback operating in nature in response to external forcing is, as pointed out in Schneider et al. (1978), made up of a complex mix of time, space, and radiation-weighted cloud changes. The best chance to realistically simulate the response of clouds to external forcing is with fully three-dimensional global climate models (GCMs). Inserting global mean cloud profiles produced by the full three-dimensional GISS model for a control and doubled-co 2 climate into the 1-D radiative convective equilibrium model of Lacis et al. (1981), Hansen et al. (1984) calculated that cloud feedback represents a significant positive feedback, made up of roughly equal contributions from decreased outgoing longwave radiation due to increased cloud altitude and increased absorbed solar radiation due to decreased cloud amount. Similar patterns of cloud changes, namely, a reduction in low and middle level clouds and an increase in the altitude of tropical high clouds, were later found in the GFDL model by Wetherald and Manabe (1988). Using the partial radiative perturbation (PRP) technique first introduced in Wetherald and Manabe (1980), they noted that the the LW cloud amount and altitude feedbacks tended to oppose one another, resulting in a positive LW cloud feedback that was roughly half as large as the positive SW cloud feedback. Roeckner et al. (1987) performed the first doubled-co 2 GCM experiments in which cloud liquid water was included prognostically, and found, after clarification by Schlesinger (1988), that increases in cloud liquid water path and optical depth brought about a positive LW optical depth feedback (due to increased high cloud emissivity) that dominated over the smaller negative SW optical depth feedback (due to increased cloud reflectivity). This result 3

5 later received further support from the uniform ±2 K sea surface temperature perturbation experiments of Taylor and Ghan (1992) for the NCAR model, but Senior and Mitchell (1993) found that phase changes from ice to water in doubled CO 2 experiments in the UK Met Office model brought about large negative SW cloud feedbacks, with contributions primarily coming from clouds at mid- and high-latitudes. Colman et al. (2001), using an earlier version of the BMRC model, performed perhaps the most comprehensive analysis of cloud feedback due to a doubling of CO 2, separating the feedback into components due to changes in cloud amount, altitude, and optical depth, with the latter further broken down into components due to changes in total water, phase, convective cloud fraction, and in-cloud temperature (a proxy for cloud geometric thickness). Using the PRP method, they computed large negative contributions to the LW cloud feedback from reductions in cloud fraction and positive contributions from changes in cloud altitude and optical depth, the latter dominated by increases in total water content of clouds. Conversely, they computed large positive contributions to the SW cloud feedback from reductions in cloud amount and increases in cloud altitude, but large negative contributions from increases in cloud optical depth, the latter being primarily due to phase changes from ice to liquid, with a smaller contribution from increases in total water content. Though the issue of inter-model spread tends to dominate contemporary discussions of cloud feedback, it is also important to identify, quantify, and understand which aspects are robust and if there are fundamental physical explanations for such responses in a warming climate. Common features to nearly all GCM studies of global warming due to increasing greenhouse gas concentrations, including the early studies described above as well as the current generation of climate models (c.f., Fig of Meehl et al. (2007)), are a decrease 4

6 in cloud amount equatorward of about 50, an increase in cloud amount poleward of 50, and an overall upward shift of clouds, features that mimic the average change in relative humidity. Another feature that is emerging as robust across models is the large increase in cloud optical depth in the region of mixed-phase clouds (roughly between 0 and -15 C) and smaller decrease at temperatures greater than freezing (Mitchell et al. (1989); Senior and Mitchell (1993); Tselioudis et al. (1998); Colman et al. (2001); Tsushima et al. (2006)). In summary, models predict opposing effects on LW and SW radiation from changes in a variety of cloud properties. The net cloud feedback thus represents the integrated effect on radiation from spatially-varying and in many cases subtle cloud amount, altitude, and optical depth responses that individually may have large magnitudes and varying degrees of compensation. Even though most models produce similar gross changes in cloud properties, estimates of cloud feedback remain widely spread relative to other feedbacks. Indeed, as first identified by Cess et al. (1989) and Cess et al. (1990), the variation in climate sensitivities predicted by GCMs is primarily attributable to inter-model differences in cloud feedbacks. This continues to be the case in contemporary climate models (Colman (2003); Soden and Held (2006); Ringer et al. (2006); Webb et al. (2006)), and recent evidence has identified the response of marine boundary layer clouds in subsidence regimes of the subtropics as primarily responsible for the inter-model spread in cloud feedback (e.g., Bony et al. (2004); Bony and Dufresne (2005); Wyant et al. (2006); Webb et al. (2006); Soden and Vecchi (2011)). As we have noted in Part I (the companion paper to this one), however, this should not be taken as evidence that other cloud responses are consistently modelled or make a narrow range of contributions to the feedback. Attribution of the mean and spread in cloud feedbacks to the nature of the cloud changes from which they arise, which is the purpose of this paper, 5

7 is a necessary first step in identifying their robust and non-robust aspects and ultimately in identifying which aspects are physically plausible and therefore realistic. In Part I of this study (Zelinka et al. (2011)) we proposed a new technique for computing cloud feedback using cloud radiative kernels along with histograms of cloud fraction partitioned into cloud top pressure (CT P) and optical depth (τ) bins by the International Satellite Cloud Climatology Project (ISCCP) simulator (Klein and Jakob (1999); Webb et al. (2001)). Perhaps the most appealing aspect of this new technique is its ability to quantify the contribution to cloud feedback from individual cloud types. However, the distinction between changes in cloud amount, altitude, and optical depth in contributing to cloud feedbacks is somewhat ambiguous. For example, we found in Part I that high cloud changes dominate the LW cloud feedback at all latitudes. This is unsurprising considering the high sensitivity of outgoing longwave radiation (OLR) to high clouds as represented by the LW cloud radiative kernel, so even if the total cloud fraction increased but the relative proportion of each cloud type in the histogram remained unchanged, high clouds would stand out as being of primary importance. It is more interesting and illuminating to quantify the contribution to the positive LW cloud feedback of rising cloud tops relative to that of changes in total cloud amount holding the vertical and optical depth distribution fixed. Similarly, it is desirable to separate the role of changes in total cloud amount from that of a shift in the cloud optical depth distribution in contributing to both LW and SW cloud feedbacks. In this study, rather than quantifying cloud feedbacks due to cloud changes within particular bins of the histogram (as was done in Part I), we quantify the cloud feedbacks arising from changes in the distribution of clouds within the histograms (i.e., clouds moving from one bin to another) and due to proportionate changes in total cloud amount (i.e., total cloud 6

8 fraction changing but the relative amounts of each cloud type in the histogram staying fixed). We perform this partitioning in an ensemble of eleven GCMs taking part in the first phase of the Cloud Feedback Model Intercomparison Project (CFMIP1), thereby providing the first model intercomparison of the LW, SW, and net cloud amount, altitude, and optical depth feedbacks Partitioning Cloud Feedback through a Decomposi- tion of Cloud Distribution Changes In this section we present the methodology we use to decompose the change in cloud fraction into components due to the proportionate change in cloud fraction, the change in CTP, and the change in τ. Each of the three feedbacks (cloud amount, altitude, or optical depth) is solely the result of changes in that component with the other two components held fixed. To separate the effect of a change in mean cloud amount from a shift in the altitude or optical depth of clouds, we divide the cloud fraction matrix into means over pressure and optical depth and departures therefrom. We note that several variants exist to define these feedbacks from ISCCP simulator output; we have chosen the simplest and most direct method for our work, but we have seen little sensitivity to the method chosen. We will explain our methodology with the help of a 2x3 example matrix in which columns represent three τ bins and rows correspond to two CTP bins. The technique described below is applied in an analogous way to the full 7x7 matrix of the ISCCP simulator output. In our example, the CTP-τ matrix of the joint histogram of cloud fraction (expressed in percent) for a single 7

9 location and month for the current climate is given by, C = 2 3 1, and an example matrix containing the change in cloud fraction, C, between the current and 2xCO 2 climate for this location and month is given by C = We define the total cloud fraction (C tot ) as: C tot = P T C, (1) p=1 τ=1 and the total change in cloud fraction ( C tot ) as: C tot = P T C, (2) p=1 τ= where P and T are the number of CTP and τ bins in the histogram (in this example, 2 and 3, respectively). The hypothetical change in cloud fraction assuming the change in total cloud fraction is distributed throughout the histogram such that the relative proportions of cloud fractions 8

10 in each CTP-τ bin remains constant is computed as: C prop = ( C tot C tot ) C. (3) The first term in Equation 3 is a scalar representing the fractional change in total cloud fraction. This decomposition isolates the contribution of changes in total cloud fraction from changes in the vertical and optical depth distribution of clouds. Using the example values, C prop = = The sum of the C prop histogram is exactly equal to the change in total cloud fraction, but constructed in such a way that the relative proportion of clouds in each bin remains constant. We will refer to C prop as the proportionate change in cloud fraction. To compute the cloud feedback associated it, which we refer to as the cloud amount feedback, we multiply this matrix by the corresponding entries of the cloud radiative kernel for its location and month. To compute the cloud altitude feedback, we first compute the hypothetical change in the distribution of cloud fractions assuming the total cloud fraction remains constant and the relative proportion of cloud fraction in each τ bin (column) remains constant. This is computed by performing the following subtraction at each pressure bin (row): C p = C 1 P P C (4) p=1 This computation takes the anomalous cloud fraction histogram and subtracts from each τ 9

11 bin (column) the mean anomaly across all CT P bins (rows). This decomposition isolates the contribution of changes in the vertical distribution of clouds from the changes in total cloud fraction and changes in the optical depth distribution of clouds. Using the example values, C p = = Note that, by definition, P C p = 0 for all τ bins and P p=1 p=1 τ=1 T C p = 0. In other words, C and C + C p have the same total amount of cloud and relative proportion of clouds in each τ bin. Multiplying C p by the cloud radiative kernel for this location and month yields the cloud altitude feedback. In a similar manner, to determine the cloud optical depth feedback, we compute the hypothetical change in the distribution of cloud fractions assuming the total cloud fraction as well as the relative proportion of clouds in each CTP bin (row) remains constant. This is computed by performing the following subtraction at each τ bin (column): C τ = C 1 T T C (5) τ=1 This computation takes the anomalous cloud fraction histogram and subtracts from each CTP bin (row) the mean anomaly across all τ bins (columns). This decomposition isolates the contribution of changes in the optical depth distribution of clouds from the changes in total cloud fraction and changes in the vertical distribution of clouds. Using the example 10

12 values, C τ = = Note that, by definition, T C τ = 0 for all CTP bins and P τ=1 p=1 τ=1 T C τ = 0. In other words, C and C + C τ have the same total amount of cloud and relative proportion of clouds in each CTP bin. Multiplying C τ by the cloud radiative kernel yields the cloud optical depth feedback. The sum of the three decomposed matrices should roughly reproduce the true C matrix, but in general, residuals remain in one or more bins. These residuals arise from coincident changes in, for example, cloud altitude and cloud optical depth, that do not unambiguously fall into one of our categories of decomposition. Summing C prop, C p, and C τ gives Note that the sum of this matrix is constrained to exactly equal the true change in cloud fraction (7 in this example). The residual is C residual = = The residual matrix sums to zero by design, but it does contribute to the cloud feedback calculation because it is multiplied with the cloud radiative kernel before being summed. 11

13 As shown below, this is generally a small contribution because the first-order components of the feedback are accounted for by the effect of cloud amount, altitude, and optical depth changes. Before continuing, it is important to recognize that aliasing can arise from partitioning cloud feedback using this decomposition. This is because the decomposed cloud fraction anomaly joint histograms may have nonzero elements even where cloud fraction anomalies are zero. A particularly egregious example would be a hypothetical large reduction in low, thin cloud fraction, with no change in the fraction of any other cloud type. This would appear in our altitude decomposition as both a negative low cloud anomaly and a positive cloud anomaly at other altitudes within the thin τ bin, and in our optical depth decomposition as both a negative thin cloud anomaly and a positive cloud anomaly at other optical thicknesses within the low CT P bin. The proportionate change in cloud fraction histogram will have negative values in every element for which the mean state cloud fraction histogram is nonzero. In other words, the effect of a change in the fraction of an individual cloud type may (1) be included in more than one decomposition, and (2) get spread among the other elements of the decomposed histograms. When multiplied by the cloud radiative kernels, this could produce appreciable cloud amount, altitude, and/or optical depth feedbacks, even though the radiative impact of that individual cloud fraction anomaly is small. Locations in which the sum of amount, altitude, and optical depth feedbacks is affected by such spreading will have nonzero residual feedbacks. Thus, care must be taken when interpretting the magnitude of amount, altitude, and optical depth feedbacks, especially where the residual term is of comparable magnitude. 12

14 Ensemble Mean Change in Cloud Properties As an aid in interpretting the contributions to cloud feedbacks from the three types of cloud changes decomposed above, in Fig. 1 we show the ensemble mean change in total cloud fraction, CTP, and the natural logarithm of τ per degree of global average surface air temperature warming. The change in ln(τ) rather than in τ is calculated because the former quantity is linearly proportional to the change in albedo (e.g., Twomey (1977)). The latter two quantities are computed by differencing the cloud fraction-weighted mean of the midpoints of each CTP or ln(τ) bin between the control and doubled CO 2 climate. For simplicity, we will refer to these as changes in CTP and ln(τ) rather than as changes in cloud fraction-weighted CT P and cloud fraction-weighted ln(τ). Henceforth, the ensemble refers to all models except the mpi echam5 model, which is excluded based on discrepancies discussed in the companion paper. Stippling indicates where 75% of the models (i.e., 9 out of 11) agree on the sign of the field plotted, and we will hereafter refer to features with this level of agreement among models as robust. Unless otherwise noted, all results in this paper are for annual mean quantities. Cloud fraction decreases nearly everywhere between 55 S and 60 N and increases nearly everywhere poleward of these latitudes (Fig. 1a). An exception to this pattern is a large region of increased cloud fraction in the central Equatorial Pacific which results from an eastward shift in convection tracking higher SSTs, though this is not a robust feature. Cloud fraction reductions are prominent in the subtropics, especially over the continents. Large increases in cloud fraction tend to occur where regions formerly covered with sea ice become open water in the warmed climate. The general pattern of a decrease in cloud fraction 13

15 equatorward of 50 is consistent with many previous studies (e.g., Wetherald and Manabe (1988); Senior and Mitchell (1993); Colman et al. (2001); Meehl et al. (2007)). Changes in CT P (Fig. 1b) are negative nearly everywhere except in regions that become dominated by low cloud types (e.g., in the Arctic and in the Central Pacific just south of the Equator), though the positive CT P changes are generally not robust. Note that these values represent the change in cloud fraction-weighted CTP; thus a location in which the cloud regime changes between the two climates (e.g., if the location switches from being a low cloud-dominated regime to a high cloud-dominated one) will exhibit large changes in this quantity. Therefore one must interpret the values on this map as representing some combination of vertical shifts in the cloud types present and changes in the frequency of occurrence of lower cloud regimes relative to higher cloud regimes. Nevertheless, the tendency for tropical clouds to systematically rise as the planet warms is consistent with theory (i.e., the fixed anvil temperature hypothesis of Hartmann and Larson (2002)), cloud resolving model experiments (Tompkins and Craig (1999); Kuang and Hartmann (2007); Harrop and Hartmann (2011)), other ensembles of GCM experiments (Zelinka and Hartmann (2010)), and observations of warming associated with El Niño (Zelinka and Hartmann (2011b)). In the extratropics, rising clouds are also consistent with a rising tropopause from a warmer troposphere and colder stratosphere due to CO 2 (Kushner et al. (2001); Santer et al. (2003); Lorenz and DeWeaver (2007)). The map of changes in ln(τ) exhibits a remarkable structure characterized by large, robust increases in ln(τ) at latitudes poleward of about 40 and generally smaller, lessrobust decreases at low latitudes (Fig. 1c). Increases in ln(τ) associated with global warming extend farther equatorward over the continents and exhibit a large seasonal cycle (not shown) 14

16 apparently driven by the larger seasonal variation in temperature relative to the oceans. As in the case of changes in CTP, it is important to keep in mind that the change in ln(τ) does not distinguish between changes in the relative proportion of lower versus higher optical depth regimes and changes in optical thickness of a given cloud type. The modeled optical depth changes are qualitatively consistent with relationships derived from ISCCP observations, in which optical thickness increases with temperature for cold low clouds but decreases with temperature for warm low clouds (Tselioudis et al. (1992) and Tselioudis and Rossow (1994)). The high latitude cloud optical thickness response is likely related to changes in the phase and/or total water contents of clouds that lead to increases in optical thickness as temperature increases. As evidence, the fractional changes, per degree of global warming, in total, ice, and liquid water paths are shown in Fig. 2. The latter quantity is computed from 244 the difference in the former two quantities. Due to limitations in the archive of CFMIP cloud output we cannot unambiguously separate these changes in grid-box mean water path into their contributions from changes in cloud amount or in-cloud water paths. Nevertheless, large, robust increases in total water path occur at high latitudes (Fig. 2a), and are clearly dominated by the liquid phase (Fig. 2c). Several lines of evidence suggest that the increase in high latitude cloud water content is realistic and that such changes should result in a clouds becoming more optically thick. In observations, the total water contents of liquid and ice clouds tend to increase with temperature (Feigelson (1978); Somerville and Remer (1984); Mace et al. (2001)) at rates approaching that of the increase in adiabatic water content (i.e., the amount of water condensed into a parcel that is a ascending moist adiabatically within a cloud) with temperature. Betts and Harshvardan (1987) demonstrated analytically that this rate is twice as large at 15

17 high latitudes than at low latitudes. Additionally, a higher freezing level associated with a warmer atmosphere promotes more liquid phase clouds which because of the Bergeron- Findeisen effect tend to precipitate less efficiently and have larger water contents than ice or mixed-phase clouds (Senior and Mitchell (1993); Tsushima et al. (2006)). Finally, even if total water content were to remain constant, the smaller size of liquid droplets relative to ice crystals tends to enhance cloud reflectivity and therefore increase optical depth Ensemble Mean Cloud Feedback Contributions Decomposed contributions to the ensemble mean LW cloud feedback are shown in Fig. 3. Increasing cloud top altitude is the dominant contributor to the LW cloud feedback, providing 0.39 W m 2 K 1 in the global mean (Fig. 3c). As in Zelinka and Hartmann (2010), we find that the ensemble mean contribution of rising tropical clouds to the LW cloud feedback (0.44 W m 2 K 1 ) is roughly twice as large as the global mean LW cloud feedback (0.21 W m 2 K 1 ). Because the Tropics represents half the area of the planet, this means that the LW cloud amount, optical depth, residual, and extra-tropical altitude feedbacks cancel in the global mean, and that the global mean feedback is simply equal to the contribution from the tropical LW cloud altitude feedback. This result is not robust across models, however. A noteworthy feature of the ensemble mean is that the 0.34 W m 2 K 1 contribution of rising cloud tops to the LW cloud feedback in the extratropics (latitude > 30 ) is only 25% smaller than that in the Tropics. These results confirm the importance of rising cloud tops to the positive LW cloud feedback, but the W m 2 K 1 global mean contribution from reductions in cloud amount (Fig. 3b) offsets 75% of the altitude 16

18 effect. We are aware of no fundamental reasons to expect the upward shift to dominate over cloud fraction reductions in bringing about a positive LW cloud feedback; indeed, in some models, the latter effect is larger (as discussed in the Section 5). The contribution of changes in cloud optical depth is smaller in the global mean than that due to changes in cloud amount and altitude, but it is nonetheless positive nearly everywhere (Fig. 3d). Notably, robust optical depth increases are the primary positive contribution to LW cloud feedback poleward of about 60 in both hemispheres, strongly opposing the locally negative altitude feedback over the polar oceans. In the global mean, the positive contribution to LW cloud feedback from optical depth increases is roughly half as large as that from cloud altitude increases. Finally, the LW cloud feedback arising from residuals in the change in cloud fraction decomposition (Fig. 3e) is negative everywhere except at very high latitudes. Its magnitude is largest where both the LW altitude and optical depth feedbacks are positive, indicating that the decomposition incorporates some cloud anomalies into both the altitude and optical depth feedbacks, causing a slight overestimate of their combined LW impact. Decomposed contributions to the ensemble mean SW cloud feedback are shown in Fig. 4. The dominant contributor to the SW cloud feedback at most locations and in the global mean is the change in cloud fraction holding the vertical and optical depth distribution fixed (Fig. 4b). With the exception of the equatorial Pacific, where non-robust increases in cloud fraction occur in the ensemble mean, robust reductions in cloud fraction at most locations between 50 S and 65 N contribute to a positive SW cloud feedback. Although cloud top altitude robustly increases, its impact on SW fluxes is negligible everywhere (Fig. 4c). The global average SW cloud altitude feedback is slightly negative, 17

19 however, owing to the slight increase in SW flux sensitivity to cloud fraction changes with decreasing cloud top pressure (c.f., Fig. 1b of Part I). In the global mean, the SW optical depth feedback is negative and considerably smaller in magnitude than the SW cloud amount feedback, but is regionally very important (Fig. 4d). Equatorward of about 40 but excluding the tropical western Pacific (where high clouds become thicker), the SW optical depth feedback is positive due to decreases in τ of lowand mid-level clouds. Consistent with this, Tselioudis et al. (1992), Tselioudis and Rossow (1994), and Chang and Coakley (2007) have shown using satellite observations that lowand midlatitude boundary layer clouds experience a decrease in optical depth as temperature increases. The most dramatic and robust feature of the optical depth feedback is the presence of large negative values at high latitudes in either hemisphere, which locally dominate the other contributions to SW cloud feedback. As discussed in the previous section, several lines of evidence suggest that cold clouds are particularly susceptible to increases in temperature that act to increase their optical depth, providing a possible physical basis for the modeled increases in τ (Fig. 1c) and for the subsequent large negative optical depth feedback at high latitudes shown here. In Fig. 5 we show the decomposed contributions to the ensemble mean net cloud feedback, which is quite strongly positive (0.57 W m 2 K 1 ). Proportionate changes in cloud fraction (Fig. 5b) contribute 0.27 W m 2 K 1 to the net cloud feedback, while rising cloud tops (Fig. 5c) contribute 0.33 W m 2 K 1. That the contribution of rising cloud tops is slightly larger than the contribution of decreasing cloud amount is an important result because one could argue that fundamental constraints exist on cloud altitude and its changes, namely, the location of radiatively-driven divergence in the tropics (Hartmann and Larson (2002); Zelinka 18

20 and Hartmann (2010)), and the height of the tropopause in the extra-tropics (Kushner et al. (2001); Santer et al. (2003); Lorenz and DeWeaver (2007)). This means that a significant portion of the ensemble mean net cloud feedback arises from relatively well-understood physical processes that are robust, not particularly sensitive to assumptions made in model parameterizations, and demonstrably positive. The contribution of optical depth changes, though small in the global mean (0.07 W m 2 K 1 ), is the primary cause of the large negative values of net cloud feedback over the Arctic and Southern Ocean (Fig. 5d). Although the global mean optical depth feedback is greater in the LW than in the SW, the net optical depth feedback map more closely resembles the SW optical depth feedback map. This is because the global mean LW optical depth feedback is the average of generally small but almost systematically positive values, whereas the global mean SW optical depth feedback is made up of locally large values that partially offset each other when averaged across different regions. These features arise because LW fluxes are only sensitive to emissivity changes of higher clouds, whereas SW fluxes are sensitive to optical depth changes at all altitudes, and warm (cold) clouds tend to become less (more) optically thick as the planet warms (e.g., Tsushima et al. (2006)). Similar to its structure in the LW, the net cloud feedback arising from residuals in the change in cloud fraction decomposition (Fig. 5e) is small and negative almost everywhere except at very high latitudes, with a global mean value of W m 2 K 1. Its magnitude is generally large where the net amount, altitude, and optical depth feedbacks share the same sign, indicating that the decomposition incorporates some cloud anomalies into all three primary feedbacks, causing a slight overestimate of their combined impact on LW+SW fluxes. 19

21 Whereas the effect of cloud amount changes on the net cloud feedback is dominated by the SW contribution (i.e., Fig. 5b looks like Fig. 4b), the effect of changes in the vertical distribution of clouds on the net cloud feedback is entirely due to the LW contribution (i.e., Fig. 5c looks like Fig. 3c). Large positive contributions from both the reduction in total cloud fraction and the upward shift of clouds produces the generally positive and robust net cloud feedback between 50 S and 65 N. The large robust negative contribution from the increase in cloud optical thickness produces the large negative cloud feedback over the Arctic and Southern Ocean. That the cloud optical depth feedback dominates over the cloud amount feedback at high latitudes is a surprising result considering that the large locally negative cloud feedback is often attributed (e.g., Weaver (2003); Vavrus et al. (2009); Wu et al. (2010)) to cloud fraction increases associated with the poleward-shifted storm track (Hall et al. (1994), Yin (2005)). Recently, Trenberth and Fasullo (2010) asserted that unrealistically small cloud fractions in the mean state of the CMIP3 models permit unrealistically large cloud fraction increases and negative cloud feedbacks over the Southern Ocean as the planet warms. Indeed, we find that appreciable robust cloud fraction increases do occur at high latitudes (Fig. 1a), and these do contribute slightly to the negative cloud feedback there (Fig. 4b). However, here we show that it is not the increase in cloud fraction but rather the shift towards brighter clouds that primarily causes this large local negative cloud feedback. If cloud optical depth rather than cloud amount is biased low, then it is quite possible that models produce unrealistic increases in cloud brightness as the planet warms, due to the fact that albedo is more sensitive to τ changes at low values of τ. Conversely, if cloud optical depth is biased high, as has been shown in several studies (e.g., Lin and Zhang (2004); Zhang et al. (2005)) then the local 20

22 negative SW optical depth feedback is in fact underestimated compared to a model with more realistic mean state optical depths, as discussed in Bony et al. (2006). In light of this and the physical mechanisms discussed above, we consider the negative cloud feedback in the S latitude band to be plausible. One must keep in mind, however, that the optical depth feedback as we have defined it does not distinguish a change in optical depth due to morphological changes in cloud type (e.g., from thin boundary layer clouds to thicker frontal clouds) that may be associated with a storm track shift from a change in optical depth due to a change in optical properties of the cloud types that are already present (e.g., thin boundary layer clouds becoming thicker). If the former is true, then the negative high latitude cloud feedback may indeed be caused by the poleward shift of the storm track, but manifested in the increase in mean optical depth rather than in cloud amount. If the latter is true, then this feedback arises from purely thermodynamic processes that lead to increased cloud liquid water content. Most likely some combination of both processes contributes to this feedback, but Figs. ESM 10 and 14 of Williams and Webb (2009) suggest that the latter process dominates. To more completely illuminate the cloud changes that result in a change from positive to negative cloud feedback with latitude over the Southern Ocean, we show the mean cloud fraction histograms in the control and doubled CO 2 climates, their difference, and the corresponding feedbacks for the S region in Fig. 6 and for the S region in Fig. 7. In both regions, the mean cloud fraction histogram primarily exhibits features of the stratocumulus, frontal, and cirrus regimes identified by Williams and Webb (2009), though clouds in the S region tend to be thinner and lower than those in the S region. The total cloud fraction is roughly 15% (absolute) larger at S. The change in cloud 21

23 fraction histogram that occurs due to climate change is remarkably different between these two regions (Figs. 6c and 7c), indicating that clouds are not simply moving from S to S. At S, the anomalous cloud fraction histogram exhibits a robust reduction in cloudiness at low levels and a robust increase in the altitude of high clouds, features that strongly resemble the global mean C (c.f., Fig. 2c of Part I). In contrast, at S, the primary change is a robust increase in cloudiness at large optical depths at all altitudes and decreases in the amount of low optical depth clouds, with an overall small increase in total cloudiness. In the S region, increased cloudiness at the highest levels contributes to a small LW cloud feedback, but the resultant large positive net cloud feedback is primarily caused by reduced SW reflection from large reductions in cloud fraction at low and mid-levels. In contrast, at S, the shift towards thicker clouds gives rise to a large positive LW cloud feedback and negative SW cloud feedback. The effects of thickening high clouds on LW and SW fluxes largely offset each other and the net cloud feedback is dominated by the large shift towards thicker clouds at the lowest levels, making it moderately negative. The changes in cloud distribution that occur in these regions likely reflect some combination of changes in the relative proportion of cloud types (e.g., stratocumulus, frontal, etc.) and changes in the properties of the individual cloud types, as shown in Williams and Webb (2009). A striking feature that is apparent from comparing panels a and b of Figs. 6 and 7, however, is the subtle nature of the changes that occur to the cloud fraction histograms in going from a control to a perturbed climate. That such nearly visually indiscernable changes in cloud distribution between the perturbed and control climates can produce large radiative fluxes is rather humbling in that it underscores an acute challenge of constraining 22

24 cloud feedbacks. The zonal and ensemble mean cloud feedbacks and their partitioning among the three components described above are shown in Fig. 8. The robust but competing effects of rising cloud tops and decreasing cloud coverage on the LW cloud feedback are apparent at most latitudes, with the LW cloud altitude feedback dominating at most latitudes, especially in the deep Tropics and midlatitudes. Proportionate cloud amount changes are the dominant contributor to the SW cloud feedback at nearly every latitude, except at high latitudes where the large increase in optical depth dominates. The relative dominance of each contributor to the net cloud feedback varies as a function of latitude, but all components are generally positive except at high latitudes where the optical depth feedback is large and negative. In general, the net residual contribution opposes the other components, most strongly where all three components have the same sign. Several features of the feedbacks shown in Fig. 8 nicely synthesize the results shown in Figs. 6 and 7 of Part I. For instance, it is apparent that the increase of high clouds at the expense of middle-level clouds (Fig 6a of Part I) strongly contributes to the extratropical maxima in the LW altitude feedback (Fig. 8a). Also, regions in which thick clouds increase at the expense of medium-thickness clouds (most prominently at latitudes greater than 50 but also in the deep Tropics, as shown in Fig 7b of Part I) are clearly the regions in which the optical depth feedback is negative (Fig. 8b). Thus the decomposition performed here provides a clear way of synthesizing the gross impact of cloud changes that may be difficult to discern from assessing the impact of individual cloud types, which can exhibit significant compensation. 23

25 Inter-Model Spread in Cloud Feedback Contributions In Figs. 9 and 10 we show global mean cloud feedback estimates and their partitioning among cloud amount, altitude, optical depth and residual components for each model and for the multi-model mean. The bar plots in Fig. 9 allow assessment of the combination of cloud responses that give rise to the global mean LW, SW, and net cloud feedbacks in each model. Fig. 10 displays these results in a more compact manner, facilitating visual comparison of the mean and spread in individual feedback components and determination of robust and non-robust feedback components. LW cloud feedback estimates span a range of 0.82 W m 2 K 1 from to 0.69 W m 2 K 1, though only the bmrc1 model has a negative value. (Note that neither of the two tests for proper simulator implementation discussed in Part I could be performed for the bmrc1 model.) In every model, proportionate reductions in global mean cloud fraction act to reduce the LW cloud feedback, with values spanning a range of 0.58 W m 2 K 1 from to W m 2 K 1. The dominant contributor to the global and ensemble mean positive LW cloud feedback is the upward shift of clouds, and increases in cloud top altitude contribute positively in all models, with values spanning a range of 0.68 W m 2 K 1 from 0.05 to 0.73 W m 2 K 1. Increases in cloud optical depth contribute positively to the LW cloud feedback in all models, with values spanning a range of 0.58 W m 2 K 1 from 0.02 to 0.60 W m 2 K 1. The LW cloud feedback arising from residuals in the change in cloud fraction decomposition spans a range of 0.58 W m 2 K 1 from to 0.12 W m 2 K 1. Even though LW cloud feedback is positive in all but one model, it is clear that the relative contributions of cloud amount changes (negative feedback) and cloud altitude changes 24

26 (positive feedback) vary significantly among models, causing this feedback to exhibit significant spread. For example, models like cccma agcm4 0 and ncar ccsm3 0 have very little cloud amount decrease and a large altitude response whereas models like bmrc1 and ipsl cm4 have the opposite proportionality. Colman and McAvaney (1997) also found a widely varying amount of compensation between these two quantities across four modified versions of the BMRC model, with resultant LW cloud feedbacks of different signs and magnitudes. This demonstrates that large uncertainties remain in the response of clouds relevant to the LW cloud feedback. This, along with the result from Part I that the spread in high-cloudinduced LW and SW cloud feedback estimates exhibits more spread than that due to low clouds, suggests that the community should not focus solely on the implications of disparate responses of low clouds for cloud feedback. SW cloud feedback estimates span a range of 1.11 W m 2 K 1 from to 0.93 W m 2 K 1. Only the gfdl mlm2 1 model, which has the largest negative optical depth feeedback, has a negative global mean SW cloud feedback. Decreasing cloud amount makes by far the largest positive contribution to the global and ensemble mean SW cloud feedback, and is the dominant positive contribution in every model except ncar ccsm3 0, with values spanning a range of 0.89 W m 2 K 1 from 0.13 to 1.02 W m 2 K 1. The range of estimates of this feedback component is the largest of all components among both the SW and LW cloud feedbacks. Increases in cloud top altitude contribute negatively to the SW cloud feedback in all models, but the values are very small, with none exceeding W m 2 K 1. SW optical depth feedback estimates, which span a range of 0.69 W m 2 K 1 from to 0.14 W m 2 K 1, are the only LW or SW non-residual contributions for which the signs are not consistent across the ensemble. The SW cloud feedback arising from residuals in the change 25

27 in cloud fraction decomposition makes a negligible contribution in the ensemble mean, but spans a range of 0.55 W m 2 K 1 from to 0.33 W m 2 K 1. Net cloud feedback estimates are positive in all models, spanning a range of 0.78 W m 2 K 1 from 0.16 to 0.94 W m 2 K 1. In every model, both the cloud amount and cloud altitude feedbacks contribute positively to the net cloud feedback. Cloud amount feedbacks span a range of 0.36 W m 2 K 1 from 0.06 to 0.42 W m 2 K 1 and cloud altitude feedbacks span a range of 0.57 W m 2 K 1 from 0.05 to 0.61 W m 2 K 1. The net optical depth feedback makes a small positive contribution in the global and ensemble mean, but individual estimates span a range of 0.43 W m 2 K 1 from to 0.31 W m 2 K 1. The net cloud feedback arising from residuals in the change in cloud fraction decomposition spans a range of 0.44 W m 2 K 1 from to 0.07 W m 2 K 1 and is generally of comparable size to the global mean net optical depth feedback. For nearly every component, the inter-model spread in net cloud feedback is systematically smaller than for the LW and SW feedbacks, indicating significant anti-correlation across models between LW and SW feedbacks. It is noteworthy that the inter-model spread in the net cloud feedback is smallest for the amount component even though SW amount feedback estimates exhibit the greatest spread of all feedback components. This again argues for caution in interpreting results about the sources of inter-model spread in cloud feedback that only consider the effect of clouds on net radiation. In most cases, regression coefficients of global mean cloud feedback components on global mean cloud feedback are statistically indistinguishable from zero due to the small sample size of only eleven models. This indicates that inter-model spread is liberally distributed between component changes and LW and SW bands with no single component playing a 26

28 dominant role. Two exceptions are the large positive regression coefficients between global mean SW cloud feedback and its amount component (0.58±0.34) and between global mean LW cloud feedback and its altitude component (0.57±0.25). We also performed a regression of the global mean feedbacks on their values from each grid point, highlighting the local contribution of each process to the spread in global mean cloud feedbacks, but at most locations, the regression slopes are statistically indistinguishable from zero Conclusions We have shown a decomposition of the change in cloud fraction histogram which separates cloud changes into components due to the proportionate change in cloud fraction holding the vertical and optical depth distribution fixed, the change in vertical distribution holding the optical depth distribution and total cloud amount fixed, and the change in optical depth distribution holding the vertical distribution and total cloud amount fixed. By multiplying the cloud radiative kernels developed in Part I with these decomposed changes in cloud fraction normalized by the change in global mean surface air temperature, we have computed the cloud amount, altitude, and optical depth feedbacks for an ensemble of eleven models taking part in CFMIP1, allowing us to assess for the first time the relative roles of these processes in determining both the multi-model mean and inter-model spread in LW, SW, and net cloud feedback. In agreement with many previous studies, a 2xCO 2 climate is associated with a reduction in total cloud amount between about 55 S and 60 N, an increase in cloud amount poleward of these latitudes, an upward shift of clouds at nearly every location, an increase in cloud 27